def test_liouvillian():
"""Test conversion of Hamiltonian/Lindblad operators into a Liouvillian"""
H = [
tensor(sigmaz(), identity(2)) + tensor(identity(2), sigmaz()),
[tensor(sigmax(), identity(2)), lambda t, args: 1.0],
[tensor(identity(2), sigmax()), lambda t, args: 1.0],
]
c_ops = [tensor(sigmam(), identity(2)), tensor(identity(2), sigmam())]
assert (
krotov.objectives.liouvillian(H[0], c_ops)
- qutip.liouvillian(H[0], c_ops)
).norm('max') < 1e-15
L = krotov.objectives.liouvillian(H, c_ops)
assert isinstance(L, list)
assert len(L) == 3
assert (L[0] - qutip.liouvillian(H[0], c_ops)).norm('max') < 1e-15
assert (L[1][0] - qutip.liouvillian(H[1][0])).norm('max') < 1e-15
assert (L[2][0] - qutip.liouvillian(H[2][0])).norm('max') < 1e-15
assert L[1][1] is H[1][1]
assert L[2][1] is H[2][1]
with pytest.raises(ValueError):
krotov.objectives.liouvillian(tuple(H), c_ops)
def two_qubit_liouvillian():
H = [
tensor(sigmaz(), identity(2)) + tensor(identity(2), sigmaz()),
[tensor(sigmax(), identity(2)), lambda t, args: 1.0],
[tensor(identity(2), sigmax()), lambda t, args: 1.0],
]
c_ops = [tensor(sigmam(), identity(2)), tensor(identity(2), sigmam())]
return krotov.objectives.liouvillian(H, c_ops)
def get_H_XY_terms(N):
""" Returns local terms, without coupling coefficients, that make up the XY hamiltonian.
returns: Hx, Hz, HPM
Hx = list of pauli X's
Hz = list of Pauli Z's
HPM = list of sigma_plus * sigma_minus """
I = qt.tensor([qt.qeye(2)] * N)
c = list(it.combinations(range(N), 2))
Hz, Hx, HPM = [0 * I for x in range(N)], [0 * I for x in range(N)
], [0 * I for x in c]
for i in range(N):
l = [qt.qeye(2)] * N
l[i] = qt.sigmaz()
Hz[i] = qt.tensor(l)
l[i] = qt.sigmax()
Hx[i] = qt.tensor(l)
for s in range(len(c)):
i, j = c[s]
l = [qt.qeye(2)] * N
l[i] = qt.sigmap()
l[j] = qt.sigmam()
HPM[s] = qt.tensor(l)
HPM[s] += HPM[s].dag()
return Hx, Hz, HPM
def e_ops_gen(params):
projectors = gen_projectors(params)
sm = tensor(sigmam(), qeye(params.c_levels))
a = tensor(qeye(2), destroy(params.c_levels))
base_e_ops = {'a': a, 'sm': sm, 'n': a.dag() * a}
e_ops = base_e_ops.copy()
for key, item in base_e_ops.items():
for i in range(2):
for j in range(2):
e_ops[key + '_' + str(i) + str(j)] = projectors[i] * item * projectors[j]
for n in range(2):
e_ops['p_q' + str(n)] = tensor(fock_dm(2, n), qeye(params.c_levels))
for n in range(params.c_levels):
e_ops['p_c' + str(n)] = tensor(qeye(2), fock_dm(params.c_levels, n))
e_ops['P_0'] = projectors[0]
e_ops['P_1'] = projectors[1]
e_ops['P_01'] = projectors[0] * projectors[1]
return e_ops
def to_matrix(self, fd):
n = num(fd)
a = destroy(fd)
ic = qeye(fd)
sz = sigmaz()
sm = sigmam()
iq = qeye(2)
ms = {
"id": tensor(iq, ic),
"a*ad" : tensor(iq, n),
"a+hc" : tensor(iq, a),
"sz" : tensor(sz, ic),
"sm+hc" : tensor(sm, ic)
}
H0 = 0
H1s = []
for (p1, p2), v in self.coefs.items():
h = ms[p1] * ms[p2]
try:
term = float(v) * h
if not term.isherm:
term += term.dag()
H0 += term
except ValueError:
H1s.append([h, v])
if not h.isherm:
replacement = lambda m: '(-' + m.group() + ')'
conj_v = re.sub('[1-9]+j', replacement, v)
H1s.append([h.dag(), conj_v])
if H1s:
return [H0] + H1s
else:
return H0
def test_jmat_12():
spinhalf = qutip.jmat(1 / 2.)
paulix = np.array([[0. + 0.j, 1. + 0.j], [1. + 0.j, 0. + 0.j]])
pauliy = np.array([[0. + 0.j, 0. - 1.j], [0. + 1.j, 0. + 0.j]])
pauliz = np.array([[1. + 0.j, 0. + 0.j], [0. + 0.j, -1. + 0.j]])
sigmap = np.array([[0. + 0.j, 1. + 0.j], [0. + 0.j, 0. + 0.j]])
sigmam = np.array([[0. + 0.j, 0. + 0.j], [1. + 0.j, 0. + 0.j]])
np.testing.assert_allclose(spinhalf[0].full() * 2, paulix)
np.testing.assert_allclose(spinhalf[1].full() * 2, pauliy)
np.testing.assert_allclose(spinhalf[2].full() * 2, pauliz)
np.testing.assert_allclose(qutip.jmat(1 / 2., '+').full(), sigmap)
np.testing.assert_allclose(qutip.jmat(1 / 2., '-').full(), sigmam)
np.testing.assert_allclose(qutip.spin_Jx(1 / 2.).full() * 2, paulix)
np.testing.assert_allclose(qutip.spin_Jy(1 / 2.).full() * 2, pauliy)
np.testing.assert_allclose(qutip.spin_Jz(1 / 2.).full() * 2, pauliz)
np.testing.assert_allclose(qutip.spin_Jp(1 / 2.).full(), sigmap)
np.testing.assert_allclose(qutip.spin_Jm(1 / 2.).full(), sigmam)
np.testing.assert_allclose(qutip.sigmax().full(), paulix)
np.testing.assert_allclose(qutip.sigmay().full(), pauliy)
np.testing.assert_allclose(qutip.sigmaz().full(), pauliz)
np.testing.assert_allclose(qutip.sigmap().full(), sigmap)
np.testing.assert_allclose(qutip.sigmam().full(), sigmam)
spin_set = qutip.spin_J_set(0.5)
for i in range(3):
assert spinhalf[i] == spin_set[i]
def setup_collapse_operators(self):
print("Setup Collapse Operators in Lindblad form", end=" ")
#Reference: http://qutip.org/docs/4.1/guide/dynamics/dynamics-time.html
collapse = []
#Empty list for collapse operators
# Collapse coefficients from the dictionary
k_Dwn = pars['kDwn']
k_Up = pars['kUp']
G_e2g = pars['Gamma_E2G']
G_g2e = pars['Gamma_G2E']
print("for the parameters")
print("kDwn = 2pi * %.3lg [GHz],\nkUp = 2pi * %.3lg [GHz]"\
%(k_Dwn/(2*np.pi), k_Up/(2*np.pi)))
print("Ge2g = %.3lg [GHz],\nGg2e = %.3lg [GHz]\n" % (G_e2g, G_g2e))
#------------------------------------------------
# Collapse operators in Lindblad Master Equation
#------------------------------------------------
a = self.a
sp = tensor(sigmap(), qeye(pars['N'])) # sigma+
sm = tensor(sigmam(), qeye(pars['N'])) # sigma-
#if isLindblad == True:
collapse.append(np.sqrt(k_Dwn) * a)
#[sqrt(2p*Gzh)]
collapse.append(np.sqrt(k_Up) * a.dag())
#[sqrt(2p*Gzh)]
collapse.append(np.sqrt(G_e2g) * sm)
#[sqrt(2p*Gzh)]
collapse.append(np.sqrt(G_g2e) * sp)
#[sqrt(2p*Gzh)]
#DISREGARDED#collapse.append(np.sqrt(Gamma_varphi) * sz);#[dimensionless]
return collapse
def _qubit_integrate(tlist, psi0, epsilon, delta, g1, g2, solver):
H = epsilon / 2.0 * sigmaz() + delta / 2.0 * sigmax()
c_op_list = []
rate = g1
if rate > 0.0:
c_op_list.append(np.sqrt(rate) * sigmam())
rate = g2
if rate > 0.0:
c_op_list.append(np.sqrt(rate) * sigmaz())
e_ops = [sigmax(), sigmay(), sigmaz()]
if solver == "me":
output = mesolve(H, psi0, tlist, c_op_list, e_ops)
elif solver == "es":
output = essolve(H, psi0, tlist, c_op_list, e_ops)
elif solver == "mc":
output = mcsolve(H, psi0, tlist, c_op_list, e_ops, ntraj=750)
else:
raise ValueError("unknown solver")
return output.expect[0], output.expect[1], output.expect[2]
def test_jumpBinary(self): tStart = 0 psi0 = qutip.basis(2, 0) psi0 = psi0.full() sp = qutip.sigmap() sm = qutip.sigmam() jumpOps = [] #Decay jumpOps.append(5 * sm) jumpOps.append(5 * sp) for i, jumpOp in enumerate(jumpOps): jumpOps[i] = jumpOp.full() jumpOps[i]= scipy.sparse.csc_matrix(jumpOps[i]) jumpOpsPaired = QJMCSetUp.jumpOperatorsPaired(jumpOps) sx = qutip.sigmax() H = sx #All objects must be in a scipy sparse format H = H.full() H = scipy.sparse.csc_matrix(H) settings = QJMCAA.Settings() settings.smallestDt = 0.0001 HEffExponentDtSet, dtSet = QJMCSetUp.HEffExponentSetProductionBinary(H, jumpOpsPaired, 0.1, settings) for _ in range(1000): r = 0.5 t, _, r = QJMCJump.jumpBinary(tStart, psi0, r, jumpOps, jumpOpsPaired, dtSet, HEffExponentDtSet) self.assertAlmostEqual(t,0.1)
def _qubit_integrate(tlist, psi0, epsilon, delta, g1, g2, solver):
H = epsilon / 2.0 * sigmaz() + delta / 2.0 * sigmax()
c_op_list = []
rate = g1
if rate > 0.0:
c_op_list.append(np.sqrt(rate) * sigmam())
rate = g2
if rate > 0.0:
c_op_list.append(np.sqrt(rate) * sigmaz())
e_ops = [sigmax(), sigmay(), sigmaz()]
if solver == "me":
output = mesolve(H, psi0, tlist, c_op_list, e_ops)
elif solver == "es":
output = essolve(H, psi0, tlist, c_op_list, e_ops)
elif solver == "mc":
output = mcsolve(H, psi0, tlist, c_op_list, e_ops, ntraj=750)
else:
raise ValueError("unknown solver")
return output.expect[0], output.expect[1], output.expect[2]
def __init__(self, N_field_levels, coupling=None, N_qubits=1):
# basic parameters
self.N_field_levels = N_field_levels
self.N_qubits = N_qubits
if coupling is None:
self.g = 0
else:
self.g = coupling
# bare operators
self.idcavity = qt.qeye(self.N_field_levels)
self.idqubit = qt.qeye(2)
self.a_bare = qt.destroy(self.N_field_levels)
self.sm_bare = qt.sigmam()
self.sz_bare = qt.sigmaz()
self.sx_bare = qt.sigmax()
self.sy_bare = qt.sigmay()
# 1 atom 1 cavity operators
self.jc_a = qt.tensor(self.a_bare, self.idqubit)
self.jc_sm = qt.tensor(self.idcavity, self.sm_bare)
self.jc_sx = qt.tensor(self.idcavity, self.sx_bare)
self.jc_sy = qt.tensor(self.idcavity, self.sy_bare)
self.jc_sz = qt.tensor(self.idcavity, self.sz_bare)
def __init__(self, N_field_levels, coupling=None, N_qubits=1):
# basic parameters
self.N_field_levels = N_field_levels
self.N_qubits = N_qubits
if coupling is None:
self.g = 0
else:
self.g = coupling
# bare operators
self.idcavity = qt.qeye(self.N_field_levels)
self.idqubit = qt.qeye(2)
self.a_bare = qt.destroy(self.N_field_levels)
self.sm_bare = qt.sigmam()
self.sz_bare = qt.sigmaz()
self.sx_bare = qt.sigmax()
self.sy_bare = qt.sigmay()
# 1 atom 1 cavity operators
self.jc_a = qt.tensor(self.a_bare, self.idqubit)
self.jc_sm = qt.tensor(self.idcavity, self.sm_bare)
self.jc_sx = qt.tensor(self.idcavity, self.sx_bare)
self.jc_sy = qt.tensor(self.idcavity, self.sy_bare)
self.jc_sz = qt.tensor(self.idcavity, self.sz_bare)
def test_mc_dtypes2():
"Monte-carlo: check for correct dtypes (average_states=False)"
# set system parameters
kappa = 2.0 # mirror coupling
gamma = 0.2 # spontaneous emission rate
g = 1 # atom/cavity coupling strength
wc = 0 # cavity frequency
w0 = 0 # atom frequency
wl = 0 # driving frequency
E = 0.5 # driving amplitude
N = 5 # number of cavity energy levels (0->3 Fock states)
tlist = np.linspace(0, 10, 5) # times for expectation values
# construct Hamiltonian
ida = qeye(N)
idatom = qeye(2)
a = tensor(destroy(N), idatom)
sm = tensor(ida, sigmam())
H = (w0 - wl) * sm.dag() * sm + (wc - wl) * a.dag() * a + \
1j * g * (a.dag() * sm - sm.dag() * a) + E * (a.dag() + a)
# collapse operators
C1 = np.sqrt(2 * kappa) * a
C2 = np.sqrt(gamma) * sm
C1dC1 = C1.dag() * C1
C2dC2 = C2.dag() * C2
# intial state
psi0 = tensor(basis(N, 0), basis(2, 1))
opts = Options(average_expect=False)
data = mcsolve(
H, psi0, tlist, [C1, C2], [C1dC1, C2dC2, a], ntraj=5, options=opts)
assert_equal(isinstance(data.expect[0][0][1], float), True)
assert_equal(isinstance(data.expect[0][1][1], float), True)
assert_equal(isinstance(data.expect[0][2][1], complex), True)
def testCOPSwithAOPS():
"""
brmesolve: c_ops with a_ops
"""
delta = 0.0 * 2 * np.pi
epsilon = 0.5 * 2 * np.pi
gamma = 0.25
times = np.linspace(0, 10, 100)
H = delta / 2 * sigmax() + epsilon / 2 * sigmaz()
psi0 = (2 * basis(2, 0) + basis(2, 1)).unit()
c_ops = [np.sqrt(gamma) * sigmam(), np.sqrt(gamma) * sigmaz()]
c_ops_brme = [np.sqrt(gamma) * sigmaz()]
a_ops = [sigmax()]
e_ops = [sigmax(), sigmay(), sigmaz()]
res_me = mesolve(H, psi0, times, c_ops, e_ops)
res_brme = brmesolve(H,
psi0,
times,
a_ops,
e_ops,
spectra_cb=[lambda w: gamma * (w >= 0)],
c_ops=c_ops_brme)
for idx, e in enumerate(e_ops):
diff = abs(res_me.expect[idx] - res_brme.expect[idx]).max()
assert_(diff < 1e-2)
def test_mcf90_dtypes2():
"mcsolve_f90: check for correct dtypes (average_states=False)"
# set system parameters
kappa = 2.0 # mirror coupling
gamma = 0.2 # spontaneous emission rate
g = 1 # atom/cavity coupling strength
wc = 0 # cavity frequency
w0 = 0 # atom frequency
wl = 0 # driving frequency
E = 0.5 # driving amplitude
N = 5 # number of cavity energy levels (0->3 Fock states)
tlist = np.linspace(0, 10, 5) # times for expectation values
# construct Hamiltonian
ida = qeye(N)
idatom = qeye(2)
a = tensor(destroy(N), idatom)
sm = tensor(ida, sigmam())
H = (w0 - wl) * sm.dag() * sm + (wc - wl) * a.dag() * a + \
1j * g * (a.dag() * sm - sm.dag() * a) + E * (a.dag() + a)
# collapse operators
C1 = np.sqrt(2 * kappa) * a
C2 = np.sqrt(gamma) * sm
C1dC1 = C1.dag() * C1
C2dC2 = C2.dag() * C2
# intial state
psi0 = tensor(basis(N, 0), basis(2, 1))
opts = Options(average_expect=False)
data = mcsolve_f90(
H, psi0, tlist, [C1, C2], [C1dC1, C2dC2, a], ntraj=5, options=opts)
assert_equal(isinstance(data.expect[0][0][1], float), True)
assert_equal(isinstance(data.expect[0][1][1], float), True)
assert_equal(isinstance(data.expect[0][2][1], complex), True)
def test_jumpOperatorsPaired(self):
#Sets up the jump operators
sp = qutip.sigmap()
sm = qutip.sigmam()
no = sp*sm
jumpOps = []
jumpOps.append(sm)
jumpOps.append(sp)
jumpOps.append(no)
for i, jumpOp in enumerate(jumpOps):
jumpOps[i] = jumpOp.full()
jumpOps[i]= scipy.sparse.csc_matrix(jumpOps[i])
#Runs the function
jumpOpsPaired = QJMCSetUp.jumpOperatorsPaired(jumpOps)
#Calculating what they should be
jumpOpsExpect = []
jumpOpsExpect.append(scipy.sparse.csc_matrix([[complex(1,0),0.0],[0.0,0.0]]))
jumpOpsExpect.append(scipy.sparse.csc_matrix([[0.0,0.0],[0.0,complex(1,0)]]))
jumpOpsExpect.append(scipy.sparse.csc_matrix([[complex(1,0),0.0],[0.0,0.0]]))
fail = -1
for i in range(len(jumpOps)):
if (jumpOpsPaired[i] - jumpOpsExpect[i]).nnz == complex(0,0):
continue
else:
fail = i
break
self.assertEqual(fail,-1)
def f(N, options):
wa = 1
wc = 0.9
delta = wa - wc
g = 2
kappa = 0.5
gamma = 0.1
n_th = 0.75
tspan = np.linspace(0, 10, 11)
Ia = qt.qeye(2)
Ic = qt.qeye(N)
a = qt.destroy(N)
at = qt.create(N)
sm = qt.sigmam()
sp = qt.sigmap()
# H = wc*qt.tensor(n, Ia) + qt.tensor(Ic, wa/2.*sz) + g*(qt.tensor(at, sm) + qt.tensor(a, sp))
Ha = g * qt.tensor(at, sm)
Hb = g * qt.tensor(a, sp)
H = [[Ha, lambda t, args: np.exp(-1j*delta*t)],
[Hb, lambda t, args: np.exp(1j*delta*t)]]
c_ops = [
qt.tensor(np.sqrt(kappa*(1+n_th)) * a, Ia),
qt.tensor(np.sqrt(kappa*n_th) * at, Ia),
qt.tensor(Ic, np.sqrt(gamma) * sm),
]
psi0 = qt.tensor(qt.fock(N, 0), (qt.basis(2, 0) + qt.basis(2, 1)).unit())
exp_n = qt.mesolve(H, psi0, tspan, c_ops, [qt.tensor(a, sp)], options=options).expect[0]
return np.real(exp_n)
def test_measure(self):
#Defines all needed variables for a test
index = 0
psi = qutip.basis(2, 1)
psi = psi.full()
eResults = []
eResults.append(numpy.zeros(1))
sp = qutip.sigmap()
sm = qutip.sigmam()
no = sp * sm
eOps = []
eOps.append(no)
for i, eOp in enumerate(eOps):
eOps[i] = eOp.full()
eOps[i] = scipy.sparse.csc_matrix(eOps[i])
histograms = []
savingSettings = QJMCAA.SavingSettings()
#Tests with no histograms set
QJMCMeasure.measure(index, psi, eResults, eOps, histograms,
savingSettings)
self.assertEqual(histograms, [])
self.assertEqual(eResults, [[0.]])
def destroy(self, mode):
"""Returns a destruction operator for the given mode
"""
ops = []
for m, i in zip(self.modes(), it.count()):
if m == mode:
ops.append(qt.sigmam())
else:
ops.append(qt.qeye(self.nfock(mode)))
return qt.tensor(ops)
def get_hamiltonian(self, controls):
H_control = self.get_hamiltonian_control(controls)
c_ops = []
if self.gamma[0] > 0.0:
c_ops.append(np.sqrt(self.gamma[0]) * q.sigmam())
if self.gamma[1] > 0.0:
c_ops.append(np.sqrt(self.gamma[1]) * q.sigmaz())
#H_noise = [self.get_hamiltonian_operator_noise(), self.noise]
return [H_control, c_ops]
def Hamiltonian(parameters, lattice):
#Constructs the operators
#(these are the essential operators that are needed for spin)
si = qutip.qeye(2)
sx = qutip.sigmax()
#sy = qutip.sigmay()
#sz = qutip.sigmaz()
sp = qutip.sigmap()
sm = qutip.sigmam()
no = sp * sm
#Constructs operators for the chain of length N
#si_list = []
sx_list = []
#sy_list = []
#sz_list = []
#sp_list = []
#sm_list = []
no_list = []
#Runs over each site defining the operator on that site
for k in range(lattice.numberOfSites):
#Puts an indentity on every site
op_list = [si] * lattice.numberOfSites
#Defines the sigma_x on site k
op_list[k] = sx
sx_list.append(qutip.tensor(op_list))
#op_list[k] = sy
#sy_list.append(qutip.tensor(op_list))
#op_list[k] = sz
#sz_list.append(qutip.tensor(op_list))
#op_list[k] = sp
#sp_list.append(qutip.tensor(op_list))
#op_list[k] = sm
#sm_list.append(qutip.tensor(op_list))
op_list[k] = no
no_list.append(qutip.tensor(op_list))
#Constructs the Hamiltonian
H = 0
#Periodic boundary conditions
#TODO define the periodic boundary conditions and closed in QJMCMath.neighbour operator with a choice
for k in range(lattice.numberOfSites):
H += (parameters.omega *
(no_list[QJMCMath.neighbour(k, lattice.numberOfSites, -1)] +
no_list[QJMCMath.neighbour(k, lattice.numberOfSites, 1)]) *
sx_list[k])
#All objects must be in a scipy sparse format
H = H.full()
H = scipy.sparse.csc_matrix(H)
return H
def test_exact_solution_for_simple_methods(method, kwargs):
# this tests that simple methods correctly determine the steadystate
# with high accuracy for a small Liouvillian requiring correct weighting.
H = qutip.identity(2)
c_ops = [qutip.sigmam(), 1e-8 * qutip.sigmap()]
rho_ss = qutip.steadystate(H, c_ops, method=method, **kwargs)
expected_rho_ss = np.array([
[1.e-16 + 0.j, 0.e+00 - 0.j],
[0.e+00 - 0.j, 1.e+00 + 0.j],
])
np.testing.assert_allclose(expected_rho_ss, rho_ss, atol=1e-16)
assert rho_ss.tr() == pytest.approx(1, abs=1e-14)
def test_collapse_with_different_tlist(self):
"""
Test if there are errors raised because of wrong tlist handling.
"""
qc = QubitCircuit(1)
qc.add_gate("X", 0)
proc = LinearSpinChain(1)
proc.load_circuit(qc)
tlist = np.linspace(0, 30., 100)
coeff = tlist * 0.1
noise = DecoherenceNoise(sigmam(), targets=0, coeff=coeff, tlist=tlist)
proc.add_noise(noise)
proc.run_state(basis(2, 0))
def construct_ham_floquet(params):
sz = tensor(sigmaz(), qeye(params.c_levels))
sx = tensor(sigmax(), qeye(params.c_levels))
sm = tensor(sigmam(), qeye(params.c_levels))
a = tensor(qeye(2), destroy(params.c_levels))
ham0 = (params.fc - params.fp) * a.dag() * a + 0.5 * (params.fa -
params.fp) * sz
ham0 += params.g * (sm * a.dag() + sm.dag() * a)
ham0 += 0.5 * params.f1 * (sm + sm.dag())
ham0 *= 2 * np.pi
return ham0
def expectationOperators(lattice, settings):
#Constructs the operators
si = qutip.qeye(2)
#sx = qutip.sigmax()
#sy = qutip.sigmay()
#sz = qutip.sigmaz()
sp = qutip.sigmap()
sm = qutip.sigmam()
no = sp * sm
#print no
#Constructs operators for the chain of length N
#si_list = []
#sx_list = []
#sy_list = []
#sz_list = []
#sp_list = []
#sm_list = []
no_list = []
#si_list.append(qutip.tensor([si] * N))
for k in range(lattice.numberOfSites):
op_list = [si] * lattice.numberOfSites
#op_list[k] = sx
#sx_list.append(qutip.tensor(op_list))
#op_list[k] = sy
#sy_list.append(qutip.tensor(op_list))
#op_list[k] = sz
#sz_list.append(qutip.tensor(op_list))
#op_list[k] = sp
#sp_list.append(qutip.tensor(op_list))
#op_list[k] = sm
#sm_list.append(qutip.tensor(op_list))
op_list[k] = no
no_list.append(qutip.tensor(op_list))
#Defines the expectation operators
e_op_list = []
#This adds on the measurement of the average population per site
e_op_list.append(no_list[0])
for i in range(1, lattice.numberOfSites):
e_op_list[0] += no_list[i]
e_op_list[0] /= lattice.numberOfSites
for i, eOp in enumerate(e_op_list):
e_op_list[i] = eOp.full()
e_op_list[i] = scipy.sparse.csc_matrix(e_op_list[i])
return e_op_list
def test_pull_572_error():
"""
brmesolve: Check for #572 bug.
"""
w1, w2, w3 = 1, 2, 3
gamma2, gamma3 = 0.1, 0.1
id2 = qutip.qeye(2)
# Hamiltonian for three uncoupled qubits
H = (w1 / 2. * qutip.tensor(qutip.sigmaz(), id2, id2) +
w2 / 2. * qutip.tensor(id2, qutip.sigmaz(), id2) +
w3 / 2. * qutip.tensor(id2, id2, qutip.sigmaz()))
# White noise
def S2(w):
return gamma2
def S3(w):
return gamma3
qubit_2_x = qutip.tensor(id2, qutip.sigmax(), id2)
qubit_3_x = qutip.tensor(id2, id2, qutip.sigmax())
# Bloch-Redfield tensor including dissipation for qubits 2 and 3 only
R, ekets = qutip.bloch_redfield_tensor(H,
[[qubit_2_x, S2], [qubit_3_x, S3]])
# Initial state : first qubit is excited
grnd2 = qutip.sigmam() * qutip.sigmap() # 2x2 ground
exc2 = qutip.sigmap() * qutip.sigmam() # 2x2 excited state
ini = qutip.tensor(exc2, grnd2, grnd2) # Full system
# Projector on the excited state of qubit 1
proj_up1 = qutip.tensor(exc2, id2, id2)
# Solution of the master equation
times = np.linspace(0, 10. / gamma3, 1000)
sol = qutip.bloch_redfield_solve(R, ekets, ini, times, [proj_up1])
np.testing.assert_allclose(sol[0], np.ones_like(times))
def c_ops_gen_jc(params, alpha=0):
c_ops = []
sm = tensor(sigmam(), qeye(params.c_levels))
a = tensor(qeye(2), destroy(params.c_levels)) + alpha
if params.gamma > 0.0:
c_ops.append(np.sqrt(2 * np.pi * params.gamma * (1 + params.n_t)) * sm)
if params.n_t > 0:
c_ops.append(np.sqrt(2 * np.pi * params.gamma * params.n_t) * sm.dag())
if params.gamma_phi > 0.0:
c_ops.append(np.sqrt(2 * np.pi * params.gamma_phi) * sm.dag() * sm)
if params.kappa > 0.0:
c_ops.append(np.sqrt(2 * np.pi * params.kappa * (1 + params.n_c)) * a)
if params.n_c > 0:
c_ops.append(np.sqrt(2 * np.pi * params.kappa * params.n_c) * a.dag())
return c_ops
def compute_free_evolution_hamiltonian(nb_qubits, nb_drives, omega, omega0,
hbar):
H_res = qt.qzero([[2, 2]])
for index_qubit in range(nb_qubits):
H_qubit_tmp = qt.Qobj(np.zeros((2, 2)))
for index_drive in range(nb_drives):
delta = omega[index_drive] - omega0[index_qubit]
H_qubit_tmp += -hbar * delta * (qt.sigmam() * qt.sigmap())
H_res = H_res + compute_multiqbt_hamil(H_qubit_tmp, nb_qubits,
index_qubit, 2)
return H_res
def expectationOperators():
#si = qutip.qeye(2)
sp = qutip.sigmap()
sm = qutip.sigmam()
no = sp * sm
eOps = []
eOps.append(no)
for i, eOp in enumerate(eOps):
eOps[i] = eOp.full()
eOps[i] = scipy.sparse.csc_matrix(eOps[i])
return eOps
def get_spin_hamiltonian(op_terms: List[Op]):
sigma_dict = {
"sigma_+": qutip.sigmap(),
"sigma_-": qutip.sigmam(),
"sigma_z": qutip.sigmaz()
}
terms = []
for op in op_terms:
qutip_list = []
for symbol in op.split_symbol:
qutip_list.append(sigma_dict[symbol])
qutip_term = qutip.tensor(qutip_list)
qutip_term *= op.factor
terms.append(qutip_term)
return sum(terms)
def hamiltonians_n_atoms_C2(NH1, NH2, N_atoms):
#Contructs the Jaynes_cummings hamiltonians for the interaction of each atom with C2
#The result is given as a list of hamiltonians in the same order as in the tensor product
hamiltonians = []
Hd_temp = qt.tensor(qt.qeye(NH1), qt.destroy(NH2))
Hc_temp = qt.tensor(qt.qeye(NH1), qt.create(NH2))
for i in range(N_atoms):
for j, H in enumerate(hamiltonians):
hamiltonians[j] = qt.tensor(qt.qeye(2), hamiltonians[j])
hamiltonians = [
.5 *
(qt.tensor(qt.sigmap(), Hd_temp) + qt.tensor(qt.sigmam(), Hc_temp))
] + hamiltonians
Hd_temp = qt.tensor(qt.qeye(2), Hd_temp)
Hc_temp = qt.tensor(qt.qeye(2), Hc_temp)
return (hamiltonians)
def test_solver_accepts_list_hamiltonian():
"""
brmesolve: input list of Qobj
"""
delta = 0.0 * 2 * np.pi
epsilon = 0.5 * 2 * np.pi
gamma = 0.25
c_ops = [np.sqrt(gamma) * qutip.sigmam()]
e_ops = pauli_spin_operators()
H = [delta * 0.5 * qutip.sigmax(), epsilon * 0.5 * qutip.sigmaz()]
psi0 = (2 * qutip.basis(2, 0) + qutip.basis(2, 1)).unit()
times = np.linspace(0, 10, 100)
me = qutip.mesolve(H, psi0, times, c_ops=c_ops, e_ops=e_ops).expect
brme = qutip.brmesolve(H, psi0, times, [], e_ops, c_ops).expect
for me_expectation, brme_expectation in zip(me, brme):
np.testing.assert_allclose(me_expectation, brme_expectation, atol=1e-8)
def construct_ham_floquet_rwa(params):
sz = tensor(sigmaz(), qeye(params.c_levels))
sx = tensor(sigmax(), qeye(params.c_levels))
sm = tensor(sigmam(), qeye(params.c_levels))
a = tensor(qeye(2), destroy(params.c_levels))
fap = params.fa - params.fp
fr = np.sqrt(fap**2 + params.f1**2)
sin_alpha = fap / np.sqrt(fap**2 + params.f1**2)
g_prime = 0.5 * params.g * (sin_alpha + 1)
ham0 = 0.5 * fr * sz + (params.fc - params.fp) * a.dag() * a + g_prime * (
sm * a.dag() + sm.dag() * a)
ham0 *= 2 * np.pi
return ham0
def __init__(self, init_state, target_state, num_focks, num_steps, alpha_list=[1]):
self.init_state = init_state
self.target_state = target_state
self.num_focks = num_focks
Sp = tensor(sigmap(), qeye(num_focks))
Sm = tensor(sigmam(), qeye(num_focks))
a = tensor(qeye(2), destroy(num_focks))
adag = tensor(qeye(2), create(num_focks))
# Control Hamiltonians
self._ctrl_hamils = [Sp + Sm, Sp * a + Sm * adag, Sp * adag + Sm * a,
1j * (Sp - Sm), 1j * (Sp * a - Sm * adag), 1j * (Sp * adag - Sm * a)]
# Number operator
self._adaga = adag * a
self.num_steps = num_steps
self.alpha_list = np.array(alpha_list + [0] * (3 - len(alpha_list)))
def test_graph_rcm_qutip():
"Graph: Reverse Cuthill-McKee Ordering (qutip)"
kappa = 1
gamma = 0.01
g = 1
wc = w0 = wl = 0
N = 2
E = 1.5
a = tensor(destroy(N), qeye(2))
sm = tensor(qeye(N), sigmam())
H = (w0-wl)*sm.dag(
)*sm+(wc-wl)*a.dag()*a+1j*g*(a.dag()*sm-sm.dag()*a)+E*(a.dag()+a)
c_ops = [np.sqrt(2*kappa)*a, np.sqrt(gamma)*sm]
L = liouvillian(H, c_ops)
perm = reverse_cuthill_mckee(L.data)
ans = np.array([12, 14, 4, 6, 10, 8, 2, 15, 0, 13, 7, 5, 9, 11, 1, 3])
assert_equal(perm, ans)
def qubit_integrate(self, tlist, psi0, epsilon, delta, g1, g2):
H = epsilon / 2.0 * sigmaz() + delta / 2.0 * sigmax()
c_op_list = []
rate = g1
if rate > 0.0:
c_op_list.append(np.sqrt(rate) * sigmam())
rate = g2
if rate > 0.0:
c_op_list.append(np.sqrt(rate) * sigmaz())
output = mesolve(H, psi0, tlist, c_op_list, [sigmax(), sigmay(), sigmaz()])
expt_list = output.expect[0], output.expect[1], output.expect[2]
return expt_list[0], expt_list[1], expt_list[2]
def testTLS(self):
"brmesolve: qubit"
delta = 0.0 * 2 * np.pi
epsilon = 0.5 * 2 * np.pi
gamma = 0.25
times = np.linspace(0, 10, 100)
H = delta/2 * sigmax() + epsilon/2 * sigmaz()
psi0 = (2 * basis(2, 0) + basis(2, 1)).unit()
c_ops = [np.sqrt(gamma) * sigmam()]
a_ops = [sigmax()]
e_ops = [sigmax(), sigmay(), sigmaz()]
res_me = mesolve(H, psi0, times, c_ops, e_ops)
res_brme = brmesolve(H, psi0, times, a_ops, e_ops,
spectra_cb=[lambda w: gamma * (w >= 0)])
for idx, e in enumerate(e_ops):
diff = abs(res_me.expect[idx] - res_brme.expect[idx]).max()
assert_(diff < 1e-2)
def testCOPS():
"""
brmesolve: c_ops alone
"""
delta = 0.0 * 2 * np.pi
epsilon = 0.5 * 2 * np.pi
gamma = 0.25
times = np.linspace(0, 10, 100)
H = delta/2 * sigmax() + epsilon/2 * sigmaz()
psi0 = (2 * basis(2, 0) + basis(2, 1)).unit()
c_ops = [np.sqrt(gamma) * sigmam()]
e_ops = [sigmax(), sigmay(), sigmaz()]
res_me = mesolve(H, psi0, times, c_ops, e_ops)
res_brme = brmesolve(H, psi0, times, [], e_ops,
spectra_cb=[], c_ops=c_ops)
for idx, e in enumerate(e_ops):
diff = abs(res_me.expect[idx] - res_brme.expect[idx]).max()
assert_(diff < 1e-2)
def run():
from mpi4py import MPI
comm = MPI.COMM_WORLD
size = comm.Get_size()
rank = comm.Get_rank()
print "Process number", rank, "of", size, "total."
neq = 2
gamma = 1.0
psi0 = qt.basis(neq,neq-1)
H = qt.sigmax()
c_ops = [np.sqrt(gamma)*qt.sigmax()]
e_ops = [qt.sigmam()*qt.sigmap()]
tlist = np.linspace(0,10,100)
ntraj=100
# One CPU per MPI process
opts = qt.Odeoptions()
opts.num_cpus = 1
# Solve
sols = mcf90.mcsolve_f90(H,psi0,tlist,c_ops,e_ops,ntraj=ntraj,options=opts)
#sols = qt.mcsolve(H,psi0,tlist,c_ops,e_ops,ntraj=ntraj,options=opts)
# Gather data
sols = comm.gather(sols,root=0)
if (rank==0):
sol = sols[0]
sol.expect = np.array(sols[0].expect)
plt.figure()
plt.plot(tlist,sols[0].expect[0],'r',label='proc '+str(0))
for i in range(1,size):
plt.plot(tlist,sols[i].expect[0],'r',label='proc '+str(i))
sol.expect += np.array(sols[i].expect)
sol.expect = sol.expect/size
plt.plot(tlist,sol.expect[0],'b',label='average')
plt.legend()
plt.show()
def spin_algebra(N, op=None):
"""Create the list [sx, sy, sz] with the spin operators.
The operators are constructed for a collection of N two-level systems
(TLSs). Each element of the list, i.e., sx, is a vector of `qutip.Qobj`
objects (spin matrices), as it cointains the list of the SU(2) Pauli
matrices for the N TLSs. Each TLS operator sx[i], with i = 0, ..., (N-1),
is placed in a :math:`2^N`-dimensional Hilbert space.
Notes
-----
sx[i] is :math:`\\frac{\\sigma_x}{2}` in the composite Hilbert space.
Parameters
----------
N: int
The number of two-level systems.
Returns
-------
spin_operators: list or :class: qutip.Qobj
A list of `qutip.Qobj` operators - [sx, sy, sz] or the
requested operator.
"""
# 1. Define N TLS spin-1/2 matrices in the uncoupled basis
N = int(N)
sx = [0 for i in range(N)]
sy = [0 for i in range(N)]
sz = [0 for i in range(N)]
sp = [0 for i in range(N)]
sm = [0 for i in range(N)]
sx[0] = 0.5 * sigmax()
sy[0] = 0.5 * sigmay()
sz[0] = 0.5 * sigmaz()
sp[0] = sigmap()
sm[0] = sigmam()
# 2. Place operators in total Hilbert space
for k in range(N - 1):
sx[0] = tensor(sx[0], identity(2))
sy[0] = tensor(sy[0], identity(2))
sz[0] = tensor(sz[0], identity(2))
sp[0] = tensor(sp[0], identity(2))
sm[0] = tensor(sm[0], identity(2))
# 3. Cyclic sequence to create all N operators
a = [i for i in range(N)]
b = [[a[i - i2] for i in range(N)] for i2 in range(N)]
# 4. Create N operators
for i in range(1, N):
sx[i] = sx[0].permute(b[i])
sy[i] = sy[0].permute(b[i])
sz[i] = sz[0].permute(b[i])
sp[i] = sp[0].permute(b[i])
sm[i] = sm[0].permute(b[i])
spin_operators = [sx, sy, sz]
if not op:
return spin_operators
elif op == 'x':
return sx
elif op == 'y':
return sy
elif op == 'z':
return sz
elif op == '+':
return sp
elif op == '-':
return sm
else:
raise TypeError('Invalid type')
def test():
gamma = 1.
neq = 2
psi0 = qt.basis(neq,neq-1)
#a = qt.destroy(neq)
#ad = a.dag()
#H = ad*a
#c_ops = [gamma*a]
#e_ops = [ad*a]
H = qt.sigmax()
c_ops = [np.sqrt(gamma)*qt.sigmax()]
#c_ops = []
e_ops = [qt.sigmam()*qt.sigmap(),qt.sigmap()*qt.sigmam()]
#e_ops = []
# Times
T = 2.0
dt = 0.1
nstep = int(T/dt)
tlist = np.linspace(0,T,nstep)
ntraj=100
# set options
opts = qt.Odeoptions()
opts.num_cpus=2
#opts.mc_avg = True
#opts.gui=False
#opts.max_step=1000
#opts.atol =
#opts.rtol =
sol_f90 = qt.Odedata()
start_time = time.time()
sol_f90 = mcf90.mcsolve_f90(H,psi0,tlist,c_ops,e_ops,ntraj=ntraj,options=opts)
print "mcsolve_f90 solutiton took", time.time()-start_time, "s"
sol_me = qt.Odedata()
start_time = time.time()
sol_me = qt.mesolve(H,psi0,tlist,c_ops,e_ops,options=opts)
print "mesolve solutiton took", time.time()-start_time, "s"
sol_mc = qt.Odedata()
start_time = time.time()
sol_mc = qt.mcsolve(H,psi0,tlist,c_ops,e_ops,ntraj=ntraj,options=opts)
print "mcsolve solutiton took", time.time()-start_time, "s"
if (e_ops == []):
e_ops = [qt.sigmam()*qt.sigmap(),qt.sigmap()*qt.sigmam()]
sol_f90expect = [np.array([0.+0.j]*nstep)]*len(e_ops)
sol_mcexpect = [np.array([0.+0.j]*nstep)]*len(e_ops)
sol_meexpect = [np.array([0.+0.j]*nstep)]*len(e_ops)
for i in range(len(e_ops)):
if (not opts.mc_avg):
sol_f90expect[i] = sum([qt.expect(e_ops[i],
sol_f90.states[j]) for j in range(ntraj)])/ntraj
sol_mcexpect[i] = sum([qt.expect(e_ops[i],
sol_mc.states[j]) for j in range(ntraj)])/ntraj
else:
sol_f90expect[i] = qt.expect(e_ops[i],sol_f90.states)
sol_mcexpect[i] = qt.expect(e_ops[i],sol_mc.states)
sol_meexpect[i] = qt.expect(e_ops[i],sol_me.states)
elif (not opts.mc_avg):
sol_f90expect = sum(sol_f90.expect,0)/ntraj
sol_mcexpect = sum(sol_f90.expect,0)/ntraj
sol_meexpect = sol_me.expect
else:
sol_f90expect = sol_f90.expect
sol_mcexpect = sol_mc.expect
sol_meexpect = sol_me.expect
plt.figure()
for i in range(len(e_ops)):
plt.plot(tlist,sol_f90expect[i],'b')
plt.plot(tlist,sol_mcexpect[i],'g')
plt.plot(tlist,sol_meexpect[i],'k')
return sol_f90, sol_mc
import cascade
gamma = 1.0 # coupling strength to reservoir
phi = 1.*np.pi # phase shift in fb loop
eps = 2.0*np.pi*gamma # eps/2 = Rabi frequency
delta = 0. # detuning
# time delay
tau = np.pi/(eps)
print 'tau =',tau
dim_S = 2
Id = qt.spre(qt.qeye(dim_S))*qt.spost(qt.qeye(dim_S))
# Hamiltonian and jump operators
H_S = delta*qt.sigmap()*qt.sigmam() + eps*(qt.sigmam()+qt.sigmap())
L1 = sp.sqrt(gamma)*qt.sigmam()
L2 = sp.exp(1j*phi)*L1
# initial state
rho0 = qt.ket2dm(qt.basis(2,0))
# times to evaluate rho(t)
tlist=np.arange(0.0001,2*tau,0.01)
def run(rho0=rho0,tau=tau,tlist=tlist):
# run feedback simulation
opts = qt.Options()
opts.nsteps = 1e7
sol = np.array([rho0]*len(tlist))
for i,t in enumerate(tlist):